in a parallelogram ABCD angle A is double of angle B find all the angles of the parallelogram
Answers
Step-by-step explanation:
In a parallelogram ABCD, angle A is double of angle B. What are the angles of the parallelogram?
In a parallelogram, the opposite angles are equal in magnitude. So angle A equals angle C, and angle B equals angle D.
(If you are wondering why the opposite angles are equal in magnitude, try drawing the diagonals AC and BD in a diagram of a parallelogram ABCD, then use congruent triangles. It is a rewarding exercise).
Let angle B = angle D = x degrees.
Then angle A = angle C = 2x degrees.
Since a parallelogram is a quadrilateral, the angles in a parallelogram add to 360 degrees,
So angle A + angle B + angle C + angle D = 360 degrees
So 2x+x+2x+x = 360
x=60 degrees so angles B and D are 60 degrees.
2x = 120 degrees so angles A and C are 120 degrees.